Polar Coordinates Calculator

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Example

Created on 2024-06-20Asked by Luna Flores (Solvelet student)

Convert the Cartesian coordinates

(3, 4)

to polar coordinates.

Solution

To convert the Cartesian coordinates

(3, 4)

to polar coordinates: 1. Calculate the polar radius

r

using the formula

r = \sqrt{x^2 + y^2}

r = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5.

2. Calculate the polar angle

\theta

using the formula

\theta = \arctan\left(\frac{y}{x}\right)

\theta = \arctan\left(\frac{4}{3}\right) \approx 0.93 \text{ radians}.

Therefore, the polar coordinates are

(5, 0.93)

(assuming angles are measured in radians). Solved on Solvelet with Basic AI Model

Some of the related questions asked by Alexander Nguyen on Solvelet

1. Convert the point

(4, \frac{\pi}{3})

from polar coordinates to rectangular coordinates.2. Graph the polar equation

r = 2 + 3\cos(\theta)

DefinitionA point in the plane is given by polar coordinates if one specifies the distance of the point from some fixed circle, the origin, we call this distance r, and the angle, theta, in radians needed to rotate a ray from the origin around the circle to the point. A point is written as (r,θ) where r is the radial and θ the angular pharmacist coordinate. Example: The polar coordainte (3, π/4) represents the point (3cos(π/4), 3sin(π/4))≈(2.12, 2.12) in Cartesian coordinates;

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